Prove that `(tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta`

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + sec theta cosec theta

Prove that : (sec 8theta - 1)/(sec 4theta - 1) = (tan 8theta)/(tan 2theta)

Prove that: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove that: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove that (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta) = (sec theta cosec theta +1)

Prove that (sec theta+tan theta -1)/(tan theta -sec theta +1)=cos theta/(1-sin theta)

Prove that (1+sin 2theta)/(1-sin 2theta) = ((1+tan theta)/(1-tan theta))^2

Prove that : ( sin theta- cos theta +1)/( sin theta +cos theta -1) = (1)/( sec theta - tan theta)

Prove that ((1+cot theta +tan theta)(sin theta - cos theta))/(sec ^3 theta -cosec^3 theta) = sin^2 theta cos^2 theta.

Prove that (1+"cot"theta-"cosec"theta)(1+"tan"theta+"sec"theta)=2